Existence and Uniqueness Solution for Nonlinear Katugampola Fractional Integro-differential Equations Involving p-Laplacian Operator

This paper is concerned with the existence and the uniqueness solution for nonlinear Katugampola fractional integro-differential equation involving the [Formula: see text]-Laplacian operator with mixed boundary conditions. Applying and combining Guo-Krasnosel’skii type fixed point principle with Banach contraction theorem, and the nonlinear alternative of Leray–Schauder type to obtain our results. Finally, we study three different examples to illustrate the effectiveness of the theoretical part.